Reply to ``Comment on `On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions','' arXiv:0711.3093v1, by A. Rosch

TL;DR

This paper defends the validity of the Luttinger theorem for Mott insulators against a recent comment, clarifying misconceptions about the theorem's applicability and the effects of weak hopping on the insulating state.

Contribution

It provides a detailed rebuttal to Rosch's critique, reaffirming the conditions under which the Luttinger theorem holds for Mott insulators.

Findings

Rosch's arguments are shown to be flawed.

The Luttinger theorem remains valid for Mott insulators under specified conditions.

Weak hopping does not necessarily destroy the Mott insulating state.

Abstract

We reply to the Comment by Achim Rosch [1] (arXiv:0711.3093v1) who challenges our finding in Ref. [2] (arXiv:0711.0952v1) with regard to the validity of the Luttinger theorem in the cases of Mott insulating N-particle ground states (even) when the chemical potential used in applying this theorem coincides with the zero-temperature limit of the chemical potential satisfying the equation of state corresponding to N particles. Rosch further argues that the strong-coupling expression for the single-particle Green function presented in Ref. [3] (arXiv:cond-mat/0602656v2) and analyzed in Ref. [2] does not imply destruction of the Mott insulating state at half-filling as a result of an arbitrary weak hopping contribution that breaks particle-hole symmetry and therefore suggests that our conclusion in Ref. [2] to the contrary were incorrect. Here we show the shortcomings of Rosch's arguments.